TURBULENCE IN HIGH ANGULAR RESOLUTION TECHNIQUES IN ASTRONOMY

Transcription

1 TURBULENCE IN HIGH ANGULAR RESOLUTION TECHNIQUES IN ASTRONOMY Invited Lecture by: JACQUES MAURICE BECKERS EMERITUS ASTRONOMER US NATIONAL SOLAR OBSERVATORY

2 WHY DO I LIKE THIS CONFERENCE? The study of temperature fluctuations on a small scale (~ 5 cm) in the Earth atmosphere is of great importance for astronomical observations. More interest by Meteorologists for such research would be most welcome.

3 DETRIMENTAL EFFECTS BY THE ATMOSPHERE ON ASTRONOMICAL OBSERVATIONS (1) ABSORPTION & SCATTERING (a) most of the electro-magnetic spectrum can only be observed from space (b) at optical wavelengths extinction limits photometry (c) scattering limits solar corona observations (2) REFRACTION (a) atmospheric dispersion/refraction (b) atmospheric turbulence seeing limits resolution (c) atmospheric turbulence scintillation/twinkling limits photometry ESO (3) POLLUTION (a) contrails limit photometry (b) mirror coating deterioration (c) thermal emissivity by dust etc.

4 DETRIMENTAL EFFECTS BY THE ATMOSPHERE ON ASTRONOMICAL OBSERVATIONS SPECKLE IMAGE OF STAR NOTICE: (i) speckle size = size of Airy disk of telescope (ii) speckles colored (diffraction phenomena) (iii) number of Speckles N sp (D/r o ) 2. D = Telescope Diameter r 0 = Fried Parameter = 10 cm for 1 500nm D = 10m N sp (iv) speckle image changes rapidly ( 10 Hz) (v) for D r 0 Airy disk N = 1 (one speckle) which dances (2) REFRACTION (a) atmospheric dispersion/refraction (b) atmospheric turbulence seeing limits resolution (c) atmospheric turbulence scintillation/twinkling limits photometry ESO/Paranal MOON NOTICE: (i) image motions (ii) Iso-Kinetic Patch [(iii) Iso-Planatic Patch ]

5 SO: WHY BOTHER WITH GROUND-BASED TELESCOPES? SPACE OBSERVATORIES HAVE: NO ATMOSPHERIC ABSORPTION : RESULTS IN FULL WAVELENGTH ACCESS BROAD COVERAGE OF PHYSICAL PROCESSES (many space observatories) NO ATMOSPHERIC SEEING : RESULTS IN HIGH RESOLUTION IMAGING RESOLVE STARS, GALAXIES PLANETS, EXOPLANETARY SYSTEMS etc. (HST) NO SCINTILLATION : RESULTS IN PRECISION PHOTOMETRY EXOPLANET TRANSITS; ASTROSEISMOLOGY (COROT) LOW THERMAL BACKGROUND : VASTLY IMPROVES INFRARED OBSERVATIONS COLD MATTER, STAR FORMATION, etc. (JWST) LOW ATMOSPHERIC SCATTERED LIGHT : HELPS CORONAGRAPHY (SOHO-LASCO) EXOPLANET IMAGING; OTHER HIGH CONTRAST OBJECTS BUT: SPACE-BASED FACILITIES ARE MANY ORDERS-OF-MAGNITUDE (100x to 1000x; more?) MORE COSTLY THAN GROUND-BASED FACILITIES COST IS THE MAIN DRIVER FOR PURSUING HIGH-RESOLUTION TECHNIQUES FOR GROUND-BASED TELESCOPES AND INTERFEROMETERS

6 WAVEFRONT DISTURBANCE BY REFRACTIVE INDEX (n) CHANGES y n 1 d n 2 Sea Level RH = 1 x = (n 2 -n 1 )*d φ = x/λ x NOTE: x, dx/dy (tilt) and d 2 x/dy 2 (curvature) are achromatic if n is λ-independent CIRCLES: RH = 1 AIR Cerro Paranal RH = 0 RADIO WAVES R.J. Mather, 2004 ANOMALOUS DISPERSION EFFECTS J H K L M NOTE: (i) in general refractive index is function of temperature & water vapor (RH) (ii) in optical/ir water vapor has little effect; T ( P & density) variations dominate seeing. (iii) in radio & far-ir astronomy water vapor variations dominate seeing (iv) anomalous dispersion effects occur mostly outside atmospheric transmission windows; they have minor effects on n variations (and do not compensate seeing as I had hoped many years ago)

7 HEIGHT VARIATION OF REFRACTIVE INDEX FLUCTUATIONS Structure Function: D n (ρ) < n(r+ρ)-n(r) 2 > r C n2 ρ 2/3 for Kolmogorov turbulence Height Variation of C n2 (h) according to Hufnagel-Valley model : Roddier (1981) day night Beckers (1993) boundary layer in daytime free atmosphere Boundary layer control is a major issue in site selection & development Actual C n2 (h) changes with location, time & wind profile In daytime lake locations and Antarctic Dome C have very low boundary layer Balloon observations show major small scale height structure in C n2 (h)

8 SEEING CONDITIONS AT DOME C Annual Variation at Different Heights 2835 m FRENCH-ITALIAN CONCORDIA STATION AT DOME C 3810 m 4100 m 3250 m WINTER SUMMER Summer/Daytime Seeing at 8.5m Height 1.3 Winter Seeing at 8.5 m Winter Seeing at 30 m AGABI et al ARNAUD et al. 2007

9 Height (meters) WINTER SUMMER? SEEING ABOVE INDICATED HEIGHT CALCULATED FROM BALLOON C n2 (h) OBSERVATIONS BEST SUMMER/DAYTIME SEEING AT 8.5 m HEIGHT (0.3 ) IS CLOSE TO FREE ATMOSPHERE SEEING (0.25 ) AVERAGE MID-SUMMER/DAYTIME SEEING (0.7 ) IS ABOUT 50% OF WINTER SEEING AT 8.5 m HEIGHT ROUGH SURFACE ENERGY BALANCE: ASSUME STEADY STATE & LOCAL CONDITIONS EXTEND EVERYWHERE IN WINTER SURFACE COLDER THAN THE AIR IN SUMMER SOLAR RADIATION EQUALIZES SURFACE AND AIR TEMPERATURES REAL SITUATION IS NON-STEADY & NON-LOCAL

10 SPATIAL POWER SPECTRUM OF WAVEFRONT DISTURBANCES L 0 l 0 Κ (m -1 ) NOTE: A LOW OUTER SCALE COMBINED WITH VERY GOOD SEEING IS A GOOD THING ESPECIALLY FOR INTERFEROMETRY inner scale of turbulence (l 0 1 cm) is of little interest for astronomy (in contrast to laser propagation) outer scale of turbulence (L 0 ) is of major interest for astronomy since: (i) it has dimensions comparable to the diameters of Large Telescopes (D 8 m for VLTs to 42 m for ELTs) (ii) it is small compared to the baselines of Optical Interferometers (e.g. VLTI 200 m ; CHARA 330 m ) L 0 depends on number of factors (like dome size, landscape, vegetation, height, telescope structure, radiation cooling, height) measured L 0 : La Palma/Hershell 2 m Sydney/SUSI 5 m Palomar/PTI 16 m Paranal 22 m Mauna Kea m OHP/France 14 m it is quite possible for a site to have multiple outer scales!!!

11 Fried Parameter r 0 definition: For Telescope Diameter D and r 0 = D the RMS Wavefront Distortion Equals 1/6 Wave Diffraction limited Image For Larger D/r o RMS Wavefront Disturbances Increase as (D/r 0 ) 5/6 Imaging Deteriorates

12 A FEW MORE EXPRESSIONS (for Zenith Angle = 0) Fried Parameter r 0 (:) λ 6/5 ( C n2 dh) -3/5 Image Size (FWHM) = λ/r 0 (radians) (:) λ -1/5 ( C n2 dh) 3/5 RMS Image Motion (:) D -1/3 C n2 dh Scintillation Index Stars= ( I RMS /I) 2 (:) λ -7/6 h 5/6 *C n2 dh Scintillation Index Sun/Moon= ( I RMS /I) 2 (:) h -1/3 *C n2 dh Time Constant τ r 0 /<V wind > Cn2 (uses Taylor approximation) Radius of Isoplanatic Patch φ r 0 /<h> Cn2 Number of Speckles (D/r o ) 2 Speckle Size = λ/d (radians) For more detail see: F. Roddier, The Effects of Atmospheric Turbulence in Optical Astronomy in Progress in Optics 19, 281, 1981.

13 REMOVING SEEING EFFECTS IN TELESCOPE IMAGING THROUGH ADAPTIVE OPTICS ( AO ): CONCEPT Originally proposed by H. Babcock (1953) Is complex servo system involving 3 parts: (1) measurement of Atmospheric Wavefront distortion on Reference Star or Beacon (2) uses a Deformable Mirror to flatten the wavefront (3) uses a Processor to couple the wavefront sensor and the deformable mirror for 0.75 arcsec seeing & 10m/s wind: λ (μm) r 0 (cm) τ 0 (sec) φ 0 ( ) Sky Coverage % % % Servo loop has to correct the wavefront with spatial resolution of r 0 and temporal resolution τ 0 (see table on the left) Reference object has to be within Isoplanatic Patch φ 0 and could be object/star itself Since r 0, τ and φ 0 increase with wavelength AO is being implemented first in the IR All major Solar Telescopes now have adaptive optics. Some Nighttime Telescopes have To provide all sky coverage at night many efforts are focused on artificial stars (Laser Beacons or Laser Guide Stars=LGSs)

14 OF SPECIAL INTEREST FOR THE TOPIC OF THIS CONFERENCE: WAVEFRONT SENSING = ATMOSPHERIC TURBULENCE SENSING! Three methods are used to sense the wavefront: (A) Wavefront Tilt sensing using Shack-Hartman Sensor image of telescope pupil For longer wavelengths (> 500 nm) wavefront tilts are close to achromatic So wavefront sensing at visible wavelengths using CCD arrays can be used for IR astronomy Number of lenslets = (D/r 0 ) for D = 10 m BMC Algorithm needed for wavefront reconstruction from wavefront tilts (e.g. Zernike expansion) (B) Wavefront Curvature Sensing using Roddier-Beckers Sensor Out-of-Focus images of original MMT mirrors showed ring- and other structure. Interpreted by JMB to correspond to wavefront curvature. F. Roddier then incorporated Out-of-Focus images as the sensor for his Curvature Adaptive Optics (C) Faucoult Knife Edge Test Ragazzoni Pyramid Wavefront Sensor

15 SOME EXAMPLES OF IMAGES RESTORED BY ADAPTIVE OPTICS STAR IMAGE NGC 1097 (ESO-VLT) no AO with AO no AO NEPTUNE (KECK TELESCOPE) SUNSPOT (NSO DUNN TELESCOPE) with AO with AO HUMAN RETINA (A. ROORDA) with AO no AO no AO with AO

16 SODIUM (& RAYLEIGH) LASER GUIDE STARS (or Laser Beacons ) Keck Observatory Uses Na-lasers at 589 nm wavelength Scattered radiation on 95 km high atomic Sodium layer creates artificial star of about 1 arcsec size This Laser Guide Star, or LGS, is not at infinity. Therefore (i) its focus is behind the nominal focus of the telescope and (ii) the light received is a cone rather than as cylinder ( Cone Effect ) The Cone Effect requires multiple LGSs to infer the wavefront coming from the actual star Laser power limits (~ 10W) the LGS brightness to V ~ 9 (depends strongly on laser properties and on Mesospheric Na density) Laser is best transmitted from the telescope center to minimize the elongation of the LGS due to the 10 km Na-layer thickness Rayleigh Scattering laser location LGS perspective elongation Keck

17 INCREASING THE CORRECTED AREA ON THE SKY BY MULTI-CONJUGATE ADAPTIVE OPTICS CONCEPT: Place N Deformable Mirrors (DM) at N Images of Conjugated Layers of the Atmosphere Example: Ground Layer and Tropopause (here: N = 2) Deform each Mirror to Correct Wavefront at that Layer Measure Wavefront of M ( N) Stars with M Wavefront Sensors (here: M = 2) Using Tomography Techniques Estimate the Wavefront Distortion at Different Layers. Technique is referred to as Atmospheric Tomography or AT =TOMOGRAPH ( CAT )

18 TRADITIONAL TOMOGRAPHY IN MEDICINE MOVING X-RAY SOURCE STATIONARY OBJECT/SUBJECT (HUMAN BODY) IMAGE PLANE MOVING PHOTOGRAPHIC FILM DEFOCUSSED BODY CAUSES BACKGROUND TOMOGRAPHIC ANGLE IS LARGE ASTRONOMY VERSION OF TRADITIONAL TOMOGRAPHY Using Natural Guide Stars. Problem: Only works in clusters of stars Using Laser Guide Stars. Problem: Need to also correct Cone Effect For N = 4 Patch Diameter increases by 2N x or 8 x SCAO MCAO

19 SOLAR S-H WAVEFRONT SENSOR FOR ATMOSPHERIC TOMOGRAPHY mm 73 mm Configuration: NSO Dunn Solar Telescope D = 76.2 cm Wavelength = 411 nm Bandwidth = 2.5 nm CCD: 2078 x 2108 pixel size 13.8 μm = arcsec FOV=127 x 127 Exp. Time = 10 ms

20 COMPUTER AIDED TOMOGRAPHY ( CAT ) IN MEDICINE USES LINEAR X-RAY SOURCE/DETECTOR ARRAYS & COMPUTER 2D IMAGE RECONSTRUCTION. ADD 1D SCANNING 3D IMAGES. NOTE: LARGE TOMOGRAPHIC ANGLE IN ATMOSPHERIC TOMOGRAPHY ASTRONOMERS USE: 2D NATURAL OR LASER GUIDE STAR ARRAYS 2D DETECTOR ARRAYS, ONE FOR EACH GUIDE STAR VERY SMALL TOMOGRAPHIC ANGLES (~ 1 arcmin) COMPUTER AIDED RECONSTRUCTION BALLOON, SCIDAR AND OTHER C n2 (h) PROFILING TOOLS GENERALLY SHOWS A NUMBER OF DOMINANT THIN OPTICAL TURBULENT LAYERS EVENTUALLY (I SUSPECT) AT & MCAO WILL INCLUDE REAL-TIME C n2 (h) KNOWLEDGE TO OPTIMIZE THE 3D TOMOGRAPHY AND THE CHOICE OF THE DM CONJUGATE HEIGHTS. 10% best seeing median seeing Mauna Kea SCIDAR

21 NAME Balloons SCIDAR G-SCIDAR S-S S SCIDAR LOLAS DASS PlaSci MOSP SODAR SNODAR A LARGE NUMBER OF C n2 (h) RANGE PROFILING TOOLS EXIST h-range h FULL NAME & COMMENTS All h greater h all h greater h low h HVR-GS all h? all h low h low h ~ 1 m Direct C 2 T (h) C 2 n (h); ; only occasionally available ~ 200 m SCIntillation Detection And Ranging requires ~ 1 to 3 m telescope & binary star ~ 200 m Generalized SCIDAR requires ~ 1 to 3 m telescope & binary star modest Single Star SCIDAR LOw LAyer Scidar needs small telescope and wide binary angle ~ 25 m High Velocity Resolution G Scidar needs small scale velocity structure with height Double-Aperture Scintillation Sensor MASS greater h? ~ 400 m? Multi-Aperture Scintillation Sensor SHABAR low h SHABAR-P all h? LuSci SLODAR low h ~ 400 m SHAdow BAnd Ranger uses scintillometer array on Sun or Moon ~ 400 m SHABAR Planet version Planetary Scintillometer (Planet version of SHABAR) ~ 400 m Lunar Scintillometer (Lunar version of SHABAR) Monitor of Wavefront Outer Scale Profiles SLOpe Detection And Ranging similar to SCIDAR but uses WFS iso scintillation SOnic Detection And Ranging uses scattering by sound waves on turbulence 1 m Surface layer NOn-Doppler Acoustic Radar

22 STATUS OF MCAO DEVELOPMENTS N=2 only ( Dual Conjugate Adaptive Optics ) Solar Observatories (KIS; NSO) using Guide- Fields and visible wavelengths (0.5 μm). Nighttime Observatories in NIR (2.2 μm) using either: (i) Natural Guide Stars (ESO-MAD/VLT) or (ii) Laser Guide Stars (GEMINI-S; being commissioned) Laboratory trials ( CfAO/Santa Cruz; Lund (Observatory) NSO-DST (0.8 m ;0.5 μm) ESO-MAD/VLT (8 m ;2.2 μm) no AO MCAO 20 Guide Fields 44

23 THE MANY FLAVORS OF ADAPTIVE OPTICS AT only MOAO Multi- Object LTAO Laser Tomography SCAO Single Conjugate MCAO & AT GLAO Ground Layer DCAO Dual Conjugate LOAO a Layer Oriented Full MCAO LOAO b Low Order ExAO Extreme PSAO Pupil Slicing MCAO & AT

24 THE MANY FORMS OF ASTRONOMICAL ADAPTIVE OPTICS AO MCAO AT SCAO DCAO GLAO Adaptive Optics Original concept proposed by Babcock ( 1959) Multi-Conjugate AO Atmospheric Tomography Single Conjugate AO Uses multiple DMs conjugated at different heights to increase FOV (Beckers, 1988) Gives 3D refractive structure of atmosphere by tomography using many guide stars (J. Beckers, 1988). Removes also the cone effect for LGS. MCAO conjugated to only one height. Dual Conjugate AO MCAO conjugated to two heights (eg( ground and tropopause). Ground-Layer AO MCAO conjugated to the ground layer (Rigaut( Rigaut,, 2001) LOAO a LOAO b MOAO LTAO ExAO PSAO Layer Oriented AO Low Order AO Multi-Object AO Laser Tomography AO Extreme AO Pupil Slicing AO MCAO using optical means on stars (instead of AT) to sense wavefronts at MCAO conjugates (Ragazzoni( Ragazzoni,, 2001) Corrects only large scale wavefront Distortions Uses separate SCAO for each of a number of objects (Hubin?). Same as SCAO/AT combination to remove cone effect for Laser Guide Stars (UofA, 2005). AO designed to have minimal light in the wings of the Point-Spread Spread-Function for High Contrast Imaging. Uses a number of DMs in segmented/sliced pupil (Beckers et al. 2006).

25 MANAGING SEEING EFFECTS IN INTERFEROMETRY There are two types of Astronomical Imaging Interferometers: (i) Monolithic Interferometers (e.g. Fizeau Experiment; MMT; LBT) Optical Path Differences (OPD) are small and constant Pupil-in = Pupil-out leads to large Field-of View (FOV) also called Homothetic Imaging Without AO Fringed Speckles AO badly needed! (ii) Non-Monolithic Interferometers (e.g. VLTI; CHARA; COAST; KECK-I ++) OPDs are very large (up to few hundred meters), vary rapidly with time and are chromatic OPD correction needs fast variable Delay Lines (DLs) with Chromatic Correction Homothetic imaging can be done but has not been implemented (yet) currently very small FOV Dual field interferometry using unresolved object in one field allows Co-Phasing (needs 2 DLs)

26 CO-PHASED AND COHERENT INTERFEROMETERS Fringe spacing varies with Wavelength Colored Fringes Coherence Length = OPD range With high fringe contrast Scan of Delay Line ( = OPD variation) Zero Optical Path Difference White Light Fringe (WLF) In the CO-PHASED MODE the OPDs in the interferometer arms have to be very close to zero (within fraction of a wavelength) This requires using the WLF on an unresolved star within the Field-Of-View of the interferometer for homothetic interferometers or a differential Delay Line on a nearby star (at VLTI this is done with PRIMA). Fringes are tracked on that star. Because the WLF is used a broad wavelength range can be used (wide color bands) In the COHERENT MODE the OPDs in the interferometer have to be within the coherence length (CL). CL = λ * (λ/ λ) = λ 2 / λ. This requires narrow color bands. Fringes have good contrast but cannot be tracked. They may be hidden in photon noise. If at least 3 interferometer arms are used one can use the Triple Correlation Technique for the combined image analysis. Average Triple Correlations Closure Phases Images (as in Radio Interferometers)

27 TRIPLE CORRELATION/BISPECTRUM ANALYSIS AND CLOSURE PHASE IMAGING How to derive phase (and amplitude) information in Coherent interferometry? No fringe tracking fringe positions change rapidly (< second scale) because of atmospheric seeing and instrumental effects. The same problem was encountered in radio astronomy in radio interferometry many years ago and solved with CLOSURE PHASE techniques (R. Jennison, 1958) It requires the use of at least 3 Interferometer arms ( with 3 telescopes) Intensity in Short Exposure Combined Image I(x,x ) (x values are vectors) Triple Correlation TC( x,x ) I(x ) I(x +x) I(x +x ) dx TC(x,x ) shows 3 correlation peaks at 3 spatial frequencies with observed phases φ, φ and φ each one consisting of the true phase Φ and an atmospheric error ε So: φ = Φ+ε ; φ = Φ+ε and φ = Φ +ε where ε = ε+ε Φ + Φ -Φ = φ + φ -φ Two of the phases e.g. Φ and Φ are related to the position of the object. They can be taken as a given like (0,0) Φ ( closure phase ) over distance x. There have to be enough photons to allow the determination of φ, φ and φ in the amount of time during which the ε values change by a fraction of 2π. NOTE: COHERENT IMAGING USING CLOSURE PHASES HAS YET NOT BEEN USED

28 CONCLUDING REMARKS 1. IMAGE RECOVERY FROM THE COMPLEX ATMOSPHERIC OPTICAL TURBULENCE DISTORTIONS IS POSSIBLE. 2. HOWEVER DOING SO IS TECHNICALLY VERY TIME CONSUMING AND EXPENSIVE 3. FOR EXAMPLE: (i) CLASSICAL AO (or SCAO) PROPOSED BY BABCOCK IN FIRST ASTRONOMICAL OPERATING SYSTEM IN 1988 (AT ESO) 4. MAJOR NEEDS NOW ARE: (ii) MULTICONJUGATE ADAPTIVE OPTICS (MCAO) WAS PROPOSED IN IN ITS SIMPLEST FORM (DCAO) IT WAS FIRST OPERATIVE IN 2004 (at NSO, Sun) & 2008 (ESO, stars). (a) Extension of AO to shorter wavelengths (b) Production of numerous ( 10 4 ) actuator, large stroke DMs as needed for ELTs and ExAO (c) Production of Adaptive Secondary Mirrors (d) Development of optimum Atmospheric Tomography algorithms (e) Construction of more powerful pulsed Sodium Lasers (f) Removal of Perspective Elongation of Laser Guide Stars (g) Moving from DCAO to full MCAO (h) In Interferometric Imaging: Development of Imaging Algorithms probably building on Radio Interferometry expertise.

29 THANK YOU!